Smallest positive number in MATLAB

I recently stumbled upon a question on Cody (#1874), which asked the user to input the smallest in MATLAB.

As per my knowledge, realmin was supposed to return the smallest number in MATLAB, however that number is the smallest normalized floating point number. According to this thread of Stack overflow, it says eps(0) returns the smallest denormal number available in MATLAB.

However, my question is how eps(0) is denormal?

> realmin returns 2.2251e-308, where as eps(0) returns 4.9407e-324

Answer 1

[Stephen23]

eps(0) returns the smallest positive non-zero floating point number, which is denormal:

format hex
eps(0)

ans = 
   0000000000000001

Normal and denormal floating point numbers are explained here:

https://blogs.mathworks.com/cleve/2014/07/07/floating-point-numbers/

https://blogs.mathworks.com/cleve/2014/07/21/floating-point-denormals-insignificant-but-controversial-2/

From the main architect of IEEE 754 (the term "gradual underflow" refers to denormal numbers):

https://people.eecs.berkeley.edu/~wkahan/ieee754status/754story.html

[Dyuman Joshi]

Thanks for all the resources, @Stephen Cobeldick. I'll try to go through them all.

[Dyuman Joshi]

Apparently I misunderstood the definition of a denormal (base 10 instead of base 2). Thank you for your answer and the links!